In an X-ray computed tomography system, an energy source irradiates X-ray beams through an object, and a detector array senses and measures the intensity of the attenuated X-ray across a thin section of the object. The X-ray intensity level incident at each detector is digitized and converted to a value representing the line integral, referred to in the art as a "projection", of the object along the X-ray path.
For third generation systems, during a scan, the X-ray source 20 and the detector array 22 rotate together about the object 24 as shown in FIG. 1. At each rotation angle, or view angle, the collected projections represent a projection profile of the object at that angle. With a set of projection profiles over many view angles, an image of the object across the scanning section can be generated in a process known as reconstruction.
Each detector channel in the array comprises an X-ray detector and associated electronic circuitry for signal amplification and digitization. The channels arc manufactured and calibrated to optimize accuracy and uniformity with respect to offset, gain, and linearity. However, even with perfect calibration, the sensitivity of each channel can be altered over time due to variation in temperature, radiation damage, and other physical conditions. Each channel therefore can exhibit an inherent error in its measurement, which can be categorized as an offset error e.sub.i in the projection value of a channel. When the intensity of the offset error e.sub.i of a channel i exceeds that of adjacent channels to a certain degree, a ring artifact is manifested in the reconstructed image. In this manner, the offset error e.sub.i is a ring-causing error.
The radius a.sub.i of a ring artifact 28 caused by channel i is equal to the distance between the projection path of the corresponding channel i and the center of rotation O, as shown in FIG. 2. Assuming this relationship, a ring artifact in an image can be identified by its corresponding channel number i. Assuming that channels are mutually independent, the offset error e.sub.i amplitudes are randomly distributed among all channels. For a given channel, the offset error e.sub.i may vary as a function of the projection amplitude. Its dependence on the projection amplitude usually remains the same within the duration of a scan. In principle, each affected channel produces a ring artifact of one channel in width, but only those channels with a sufficiently large offset e.sub.i generate visible ring artifacts in the image. With a random distribution of offset error e.sub.i, the visible rings are likewise randomly distributed.
In conventional techniques for mitigating offset error, the offset error e.sub.i can be estimated from the projection data, based on the assumptions that the same degree of error occurs over successive view angles, and that the error is independent of the performance of adjacent channels. Furthermore, it is known that the projection data vary gradually as a function of detector channel. Therefore, if projection data are plotted as two-dimensional data (channel number vs. view angle), a low-pass filter can be employed to average the projection values over a number of successive view angles. A high-pass filter can then be applied along the channel number dimension to filter offset error out of the object's projection profile. Linear filtering alone may be insufficient for separating the offset error from the object profile. Therefore, additional nonlinear filtering is often necessary to discriminate offset error from the object profile.
In the conventional techniques, the error offset responsible for causing a single-channel ring can be estimated with fair accuracy. The estimated error is then subtracted from the projection values collected at that channel. Following correction of all channels, the reconstructed image is free of single-channel rings. However, it is quite common for an image to exhibit multiple-channel ring artifacts. The high-pass filter is incapable of yielding an adequate estimate of this multiple-channel error, because such a filter is designed for determining single-channel error. Consequently, multiple-channel rings are not fully corrected, and the resulting image therefore includes reminiscent rings.
In principle, the wider multiple-channel rings are unlikely to occur if the detector channel offset errors are completely independent of each other. However, detectors located in proximity tend to stay in the same physical condition and their corresponding offsets tend to drift together, particularly in a system having solid-state detectors. The intensities of wide multiple-channel rings are generally much weaker than those of the single-channel rings, since the common offset error over multiple-channels is, on average, smaller than a single-channel offset error. Furthermore, as a result of high-pass filtering in the convolution operation performed during the reconstructing process, the intensity of the wide ring artifact does not stand out as much as that of a single-channel ring of the same offset error amplitude. The presence of wide rings is often visible in images of objects of uniform structure, such as water phantoms. However, due to their relatively low intensity, they are less visible in an image of a non-uniform object, for example, human body images.
In principle, existing filtering ring artifact correction techniques can be extended to correct for the wide rings. However, conventional filters are specifically designed to filter out single-channel error. In order to filter out rings of variable multiple-channel width, a set of filters are required, each tailored to handle a specific width. Since a ring can be several channels in width, the total amount of computations required may be several times that needed for single-channel ring correction, leading to an impractical computing time. It is also questionable whether such a solution would lead to effective correction of wide rings, and worse, it is quite possible that this technique of curing the wide ring artifacts may reintroduce narrow ring artifacts back into the image.
Considering the aforementioned problems, little has been done to address the correction of wide rings in the past. The intensity of these wide rings are not as strong as single-channel rings, and with accurate and frequent calibration, they do not pose a serious problem. However, as systems improve and become increasingly sophisticated, it is desirable to be able to correct them. If they are correctable, the requirements for calibration can also be relaxed.